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We can do this without referring to Ramanujan's formula: Doing some numerical experimentation, we suspect that the answer is 3. We can prove this result by repeatedly using the formula x = ( x + 2 ) + ( x − 2 ) ( x + 1 ) , always applying it to the last number appearing in an expression: 3 = 5 + 1 ∗ 4 = 5 + 1 6 + 2 ∗ 5 = 5 + 1 6 + 2 7 + 3 ∗ 6 =...
brilliant!.. the level of this problem should be more than this..
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true that.
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It is very easy to approximate the answer as 3, which is why the problem rating is so low.
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@Daniel Liu – Can you please tell how you approximated the answer.
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@Ankith A Das – Let's say that 6 + 2 . . . ≈ 9 , so 5 + 6 + 2 . . . ≈ 8 so 5 + 6 + 2 . . . ≈ 3
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5 + 1 6 + 2 7 + 3 8 + 4 9 + 5 … U s i n g R a m a n u j a n ′ s n e s t e d r a d i c a l f o r m u l a x + n + a = a x + ( a + n ) 2 + x a ( x + n ) + ( a + n ) 2 + ( x + n ) . . . W e c a n s e e t h a t x = 1 t h e n x + n = 2 1 + n = 2 ; n = 1 S u b s t i t u t i n g x a n d n i n a x + ( a + n ) 2 a ( 1 ) + ( a + 1 ) 2 = 5 a = 1 x + n + a = 1 + 1 + 1 = 3